License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
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DOI: 10.4230/LIPIcs.CSL.2011.67
URN: urn:nbn:de:0030-drops-32233
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2011/3223/
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Bès, Alexis ; Carton, Olivier

Algebraic Characterization of FO for Scattered Linear Orderings

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Abstract

We prove that for the class of sets of words indexed by countable scattered linear orderings, there is an equivalence between definability in first-order logic, star-free expressions with marked product, and recognizability by finite aperiodic semigroups which satisfy some additional equation.

BibTeX - Entry

@InProceedings{bs_et_al:LIPIcs:2011:3223,
  author =	{Alexis B{\`e}s and Olivier Carton},
  title =	{{Algebraic Characterization of FO for Scattered Linear Orderings}},
  booktitle =	{Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL},
  pages =	{67--81},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-32-3},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{12},
  editor =	{Marc Bezem},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2011/3223},
  URN =		{urn:nbn:de:0030-drops-32233},
  doi =		{10.4230/LIPIcs.CSL.2011.67},
  annote =	{Keywords: linear orderings, first-order logic, semigroups, rational sets}
}

Keywords: linear orderings, first-order logic, semigroups, rational sets
Collection: Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL
Issue Date: 2011
Date of publication: 31.08.2011

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